Question

Dante is holding a local dance for the community. He pays $125 to rent the local firehouse for the evening. He also must pay $3 for insurance for every guest at the party. If Dante charges $8 for entry to the dance, how many tickets must sell in order to recover all the money he has to pay?

Answer 1

Dante should sell 25 tickets in order to recover all money he paid.

Explanation:

Let us assume Dante has to sell m tickets to recover all the money he pays.

Now, the amount paid to local firehouse = $125

The per person insurance costs = $ 3

So, the insurance of M guests cost = M x ( The cost of insurance per person)

= M x ( $3) = 3M

So, the cost of insurance of M guest = 3 M .... (1)

Also, The per person ticket costs = $ 8

So, the cost of M guests tickets = M x ( The cost per person)

= M x ( $8) = 8 M

So, the cost of tickets of M guest = 8 M .... (2)

Now, the total cost paid by Dante in organizing

= Amount paid to FIRE house + total Insurance cost of M people

= $125 + 3 M

And, the amount he receives after selling M tickets = 8 M

Now, for M tickets: The amount Spend = Amount Earned

⇒ 125 + 3 M = 8 M

or, 125 = 5 M

or, M = 125/5 = 25 ⇒M = 25

Hence, Dante should sell 25 tickets in order to recover all the money he has to pay.